What is the cost when 150 units are produced?

AI Thread Summary
The discussion revolves around calculating the cost, revenue, and profit functions for a bicycle parts manufacturer with fixed costs of $25,000, production costs of $21.75 per unit, and a selling price of $325 per unit. The correct cost function is C(x) = 21.75x + 25,000, while the revenue function is R(x) = 325x. The profit function is derived as P(x) = R(x) - C(x). The participants are encouraged to evaluate these functions to find the cost of producing 150 units, which requires substituting x with 150 in the cost function. Overall, the thread emphasizes the importance of understanding the relationships between fixed costs, variable costs, and revenue to accurately compute financial metrics.
nae99
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Homework Statement



A manufacturer of bicycle parts, has a monthly fixed cost of $25 000, a production cost of $21.75 per unit and a selling price of $325 per unit.
a) Cost function
b) Revenue function
c) Profit function
d) Break-even point
f) Cost when 150 units are produced.

Homework Equations





The Attempt at a Solution


a) 25 000 (x) =$21.75 (x) + $325
 
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nae99 said:

Homework Statement



A manufacturer of bicycle parts, has a monthly fixed cost of $25 000, a production cost of $21.75 per unit and a selling price of $325 per unit.
a) Cost function
b) Revenue function
c) Profit function
d) Break-even point
f) Cost when 150 units are produced.

Homework Equations

The Attempt at a Solution


a) 25 000 (x) =$21.75 (x) + $325

You need to put in more steps to lessen your confusion. Call the cost, revenue and profit functions for x units C(x), R(x), and P(x). To answer the first three parts, finish these three equations:

C(x) = ?
R(x) = ?
P(x) = ?

with formulas in terms of x on the right side. Then we can talk.
 
Your equation a) contains a couple of mistakes. The monthly fixed costs are constant: no matter how many bicycles are made, it takes $25000 to keep the plant open and ready for production. The $325 selling price for each bike is not charged to the company unless it decides to buy a bike at retail.

You should also try to answer the other parts of the problem.
 
LCKurtz said:
You need to put in more steps to lessen your confusion. Call the cost, revenue and profit functions for x units C(x), R(x), and P(x). To answer the first three parts, finish these three equations:

C(x) = ?
R(x) = ?
P(x) = ?

with formulas in terms of x on the right side. Then we can talk.

i am not sure about the formulas
C(x)= mx+b
R(x) = mx
P(x) = R(x) - C(x)
 
LCKurtz said:
You need to put in more steps to lessen your confusion. Call the cost, revenue and profit functions for x units C(x), R(x), and P(x). To answer the first three parts, finish these three equations:

C(x) = ?
R(x) = ?
P(x) = ?

with formulas in terms of x on the right side. Then we can talk.

nae99 said:
i am not sure about the formulas
C(x)= mx+b
R(x) = mx
P(x) = R(x) - C(x)

So what are m and b in this problem?
 
LCKurtz said:
So what are m and b in this problem?

m= selling price
b= units

C(x)= 325x+21.75
 
nae99 said:
m= selling price
b= units

i think

But x is the number of units. I think you are just guessing. You just need to think about it some more. Here's a simpler example. If it costs me $100 to open my shop and $25 to build each widget, how much will it cost me total to build 3 widgets?
 
LCKurtz said:
But x is the number of units. I think you are just guessing. You just need to think about it some more. Here's a simpler example. If it costs me $100 to open my shop and $25 to build each widget, how much will it cost me total to build 3 widgets?

it will cost $75
 
ok so it would be
C(x) = 325(x)+25 000
 
  • #10
LCKurtz said:
But x is the number of units. I think you are just guessing. You just need to think about it some more. Here's a simpler example. If it costs me $100 to open my shop and $25 to build each widget, how much will it cost me total to build 3 widgets?

nae99 said:
it will cost $75

What about the $100 rent (or salaries or whatever for that day)?

Once you answer that, what is the answer to build n widgets?

And if I sell n of them for $150 each, how much revenue will I get?
 
  • #11
nae99 said:
ok so it would be
C(x) = 325(x)+25 000

NO! What does the $325 have to do with the cost?
 
  • #12
LCKurtz said:
NO! What does the $325 have to do with the cost?

$325 is the selling price
i don't know the formula, i think once i have the formula i will be able to do it
 
  • #13
LCKurtz said:
But x is the number of units. I think you are just guessing. You just need to think about it some more. Here's a simpler example. If it costs me $100 to open my shop and $25 to build each widget, how much will it cost me total to build 3 widgets?

LCKurtz said:
What about the $100 rent (or salaries or whatever for that day)?

Once you answer that, what is the answer to build n widgets?

And if I sell n of them for $150 each, how much revenue will I get?

nae99 said:
i don't know the formula, i think once i have the formula i will be able to do it

I am trying to help you understand how to figure out the formula. It would help if you would answer the widget questions I have posted above. Please don't edit some previous post; just reply to this one.
 
  • #14
LCKurtz said:
I am trying to help you understand how to figure out the formula. It would help if you would answer the widget questions I have posted above. Please don't edit some previous post; just reply to this one.

it will cost $175 to build n widgets

And if u sell n of them for $150 each, would get $450
 
  • #15
nae99 said:
it will cost $175 to build n widgets

And if u sell n of them for $150 each, would get $450

Those are the answers for 3 widgets. What are the answers for n?
 
  • #16
LCKurtz said:
Those are the answers for 3 widgets. What are the answers for n?

would n=3
 
  • #17
nae99 said:
would n=3

You need to use n in the formulas instead of 3 if that's what you are asking. What do you get for both questions?
 
  • #18
LCKurtz said:
You need to use n in the formulas instead of 3 if that's what you are asking. What do you get for both questions?

that's the thing, i don't know the formula
 
  • #19
nae99 said:
that's the thing, i don't know the formula

But you do know the formula if you just think about it. You answered both my questions for 3 widgets. You did a mental calculation to get those answers. You did a calculation using the number 3. Can you do the same calculation for 4 widgets? 5? 6?

Just describe the calculation you did but use n instead of a specific number. I know you can do it.
 
  • #20
LCKurtz said:
But you do know the formula if you just think about it. You answered both my questions for 3 widgets. You did a mental calculation to get those answers. You did a calculation using the number 3. Can you do the same calculation for 4 widgets? 5? 6?

Just describe the calculation you did but use n instead of a specific number. I know you can do it.

is it
n= 25(n) + 100
 
  • #21
nae99 said:
is it
n= 25(n) + 100

Almost. Since this is the Cost to make n widgets, why are you calling it n on the left side? Fix that and answer the second question; how much Revenue would I get from selling n widgets?
 
  • #22
LCKurtz said:
Almost. Since this is the Cost to make n widgets, why are you calling it n on the left side? Fix that and answer the second question; how much Revenue would I get from selling n widgets?

Revenue =150(n)
 
  • #23
LCKurtz said:
Almost. Since this is the Cost to make n widgets, why are you calling it n on the left side? Fix that and answer the second question; how much Revenue would I get from selling n widgets?

nae99 said:
Revenue =150(n)

OK, finally you have cost and revenue:
C=100+25n and R = 150n so you can figure out profit =R - C.

Now notice that to get the total cost you took the fixed cost plus the number of items times the individual item cost. To get the revenue you took the selling price times the number of items. These formulas are no doubt in your text. To work your original problem you do the same thing. In that problem you are using x instead of n but the logic is the same and only the numbers are different.
 
  • #24
LCKurtz said:
OK, finally you have cost and revenue:
C=100+25n and R = 150n so you can figure out profit =R - C.

Now notice that to get the total cost you took the fixed cost plus the number of items times the individual item cost. To get the revenue you took the selling price times the number of items. These formulas are no doubt in your text. To work your original problem you do the same thing. In that problem you are using x instead of n but the logic is the same and only the numbers are different.

so for my original question it would be

C=25 000+325(21.75)
R=325(21.75)
 
  • #25
LCKurtz said:
OK, finally you have cost and revenue:
C=100+25n and R = 150n so you can figure out profit =R - C.

Now notice that to get the total cost you took the fixed cost plus the number of items times the individual item cost. To get the revenue you took the selling price times the number of items. These formulas are no doubt in your text. To work your original problem you do the same thing. In that problem you are using x instead of n but the logic is the same and only the numbers are different.

nae99 said:
so for my original question it would be

C=25 000+325(21.75)
R=325(21.75)

Have you not understood anything I have said? What did n represent in my example? In my example everything is a function of n. There are no variables in your answer and it looks like you are just blindly plugging in all your numbers -- guessing again. Read the paragraphs I have quoted here and try to understand them.
 
  • #26
No. Look at what LCKurtz has in post #23. Your Cost and Revenue functions should be in terms of the number of units that are manufactured.

In other words, C and R should involve x.
 
  • #27
LCKurtz said:
Have you not understood anything I have said? What did n represent in my example? In my example everything is a function of n. There are no variables in your answer and it looks like you are just blindly plugging in all your numbers -- guessing again. Read the paragraphs I have quoted here and try to understand them.

C=25 000 + 325(x)

R= 325(x)

is that any good
 
  • #28
That's closer, but still not right. As you have it, it costs them $325 to make one bike, and they sell it for the same price.
 
  • #29
Mark44 said:
That's closer, but still not right. As you have it, it costs them $325 to make one bike, and they sell it for the same price.

i am confused
C=25 000 + 21.75(x)
is that correct
 
  • #31
Mark44 said:
Yes, that's better.

and Revenue will be
R = 21.75(x)
 
  • #32
No, you had it correct before in post #27. The company can't make any profit if they sell the bikes for the same as it costs to make them.
 
  • #33
Mark44 said:
No, you had it correct before in post #27. The company can't make any profit if they sell the bikes for the same as it costs to make them.

ok so working out the cost function would it be

C(x) = 21.75(x) + 25 000
C(325) = 21.75(325) + 25 000
C(325) = 7068.75 + 25 000
C(325) = 32 068.75
 
  • #34
nae99 said:
ok so working out the cost function would it be

C(x) = 21.75(x) + 25 000
Stop here.

Why are you calculating C(325)?
nae99 said:
C(325) = 21.75(325) + 25 000
C(325) = 7068.75 + 25 000
C(325) = 32 068.75

Your problem is to find these:
a) Cost function. It is C(x) = 21.75x + 25,000
b) Revenue function. You have it - it is R(x) = 325x
c) Profit function
d) Break-even point
e) Cost of producing 150 bikes
 
  • #35
ok, so i should only put in the functions which are
c) Profit function P(x) = 325x - 25021.75x
d) Break-even point 325x= 21.75x + 25 000
e) Cost of producing 150 bikes C = 150x + 25 000
 
  • #36
These are all wrong.
nae99 said:
ok, so i should only put in the functions which are
c) Profit function P(x) = 325x - 25021.75x
How did you get this? P(x) = R(x) - C(x).
nae99 said:
d) Break-even point 325x= 21.75x + 25 000
The break-even point is the value of x for which C(x) = R(x).
nae99 said:
e) Cost of producing 150 bikes C = 150x + 25 000
The cost function is C(x) = 21.25x + 25,000. What is C(150)?
 
  • #37
ok, so the formulas are
profit = Revenue - cost P(x) = R(x) - C(x)

break even = C(x) = R(x)
are these right
and the Cost of producing 150 bikes will be C(150) = 21.25x + 25,000
 
  • #38
nae99 said:
ok, so the formulas are
profit = Revenue - cost P(x) = R(x) - C(x)
Yes, but what is P(x) in terms of the formulas for R(x) and C(x)?
nae99 said:
break even = C(x) = R(x)
are these right
Yes, and I wrote this already. Your job is to find the value of x for which C(x) = R(x).
nae99 said:
and the Cost of producing 150 bikes will be C(150) = 21.25x + 25,000
No, what you have on the right is C(x), not C(150). Evaluate your function at x = 150. Your answer should be a number - no x.
 
  • #39
You are just guessing. Plug in numbers until you get corrected enough times that the answer is correct. But you are showing absolutely no understanding of what you are doing. You will never learn how to analyze this kind of problem with that approach.

At this point, my best advice to you is to schedule an appointment with your teacher. I have done everything I can short of working the problem for you, which I will not do.
 
Last edited:
  • #40
d) Break-even point 325x= 21.75x + 25 000

The break-even point is the value of x for which C(x) = R(x)

R(x) = C(x)
325x = 21.75x + 25 000
325x - 21.75x = 25 000
13.25x = 25 000
13.25x/13.25 = 25 000/13.25
x = 1886.79
 
  • #41
nae99 said:
d) Break-even point 325x= 21.75x + 25 000

The break-even point is the value of x for which C(x) = R(x)

R(x) = C(x)
325x = 21.75x + 25 000
325x - 21.75x = 25 000
13.25x = 25 000
I can't even guess how you got 13.25x from the line above.
nae99 said:
13.25x/13.25 = 25 000/13.25
x = 1886.79
This is way off.
 
  • #42
Mark44 said:
I can't even guess how you got 13.25x from the line above.

This is way off.

oh sorry its suppose to be
325x = 21.75x + 25 000
325x - 21.75x = 25 000
303.25x = 25 000
303.25x/303.25 = 25 000/303.25
x= 82.440
 
  • #43
That looks like the right number. What does it represent?
 
  • #44
Mark44 said:
That looks like the right number. What does it represent?

it represent the break-even point
 
  • #45
Mark44 said:
That looks like the right number. What does it represent?

it represent the break-even point
 
  • #46
Have you done the last part yet? I.e., find the cost of making 150 bikes?
 
  • #47
Mark44 said:
Have you done the last part yet? I.e., find the cost of making 150 bikes?

No, because i am confuse
 
  • #48
Mark44 said:
a) Cost function. It is C(x) = 21.75x + 25,000

All you need to do is evaluate C(150) using the formula above.
 
  • #49
I don't think there is any need to continue this.
 

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